Introduction

Additional electromagnetic physics processes for photons, electrons, hadrons and ions have been implemented in Geant4 in order to extend the validity range of particle interactions to lower energies than those available in the standard Geant4 electromagnetic processes [1,2,3]. Because atomic shell structure is more important in most cases at low energies than it is at higher energies, the low energy processes make direct use of shell cross section data. The standard processes, which are optimized for high energy physics applications, rely on parameterizations of these data.

The low energy processes include the photo-electric effect, Compton scattering, Rayleigh scattering, gamma conversion, bremsstrahlung and ionization. Fluorescence of excited atoms is also considered.

Some features common to all low energy processes currently implemented in Geant4 are summarized in this section. Subsequent sections provide more detailed information for each process.

Physics

The low energy processes of Geant4 represent electromagnetic interactions at lower energies than those covered by the equivalent Geant4 standard electromagnetic processes.

The current implementation of low energy processes is valid for energies down to 250 eV (and can be used up to approximately 100 GeV), unless differently specified. It covers elements with atomic number between 1 and 99.

All processes involve two distinct phases:

• the calculation and use of total cross sections, and
• the generation of the final state.

Both phases are based on the theoretical models and on exploitation of evaluated data.

Data Sources

The data used for the determination of cross-sections and for sampling of the final state are extracted from a set of publicly distributed evaluated data libraries:

• EPDL97 (Evaluated Photons Data Library) [4];
• EEDL (Evaluated Electrons Data Library) [5];
• EADL (Evaluated Atomic Data Library) [6];
• stopping power data [7,8,9,10];
• binding energy values based on data of Scofield [11].

Evaluated data sets are produced through the process of critical comparison, selection, renormalization and averaging of the available experimental data, normally complemented by model calculations. These libraries provide the following data relevant for the simulation of Geant4 low energy processes:

• total cross-sections for photoelectric effect, Compton scattering, Rayleigh scattering, pair production and bremsstrahlung,
• subshell integrated cross sections for photo-electric effect and ionization,
• energy spectra of the secondaries for electron processes,
• scattering functions for the Compton effect,
• form factors for Rayleigh scattering,
• binding energies for electrons for all subshells,
• transition probabilities between subshells for fluorescence and the Auger effect, and
• stopping power tables.

The energy range covered by the data libraries extends from 100 GeV down to 1 eV for Rayleigh and Compton effects, down to the lowest binding energy for each element for photo-electric effect and ionization, and down to 10 eV for bremsstrahlung.

Distribution of the Data Sets

The author of EPDL97 [4], who is also responsible for the EEDL [5] and EADL [6] data libraries, Dr. Red Cullen, has kindly permitted the libraries and their related documentation to be distributed with the Geant4 toolkit. The data are reformatted for Geant4 input. They can be downloaded from the source code section of the Geant4 page: http://cern.ch/geant4/geant4.html.

The EADL, EEDL and EPDL97 data-sets are also available from several public distribution centres in a format different from the one used by Geant4 [12].

Stopping power data are taken from publications [7,8,9,10].

Calculation of Total Cross Sections

The energy dependence of the total cross section is derived for each process from the evaluated data libraries. Since the libraries provide cross sections for a set of discrete incident energies, the total cross section at a given energy, $E$, is obtained by interpolation according to the formula [13]:

$$\log(\sigma(E)) = {log(\sigma_1)log(E_2/E) + log(\sigma_2)log(E/E_1) \over log(E_2/E_1)}$$ (11.1)

where $E_1$ and $E_2$ are respectively the closest lower and higher energy for which data ($\sigma_1$ and $\sigma_2$) are available.

For each process a production threshold energy is defined; by default it is set to the low end of the energy validity range of the process (250 eV in the current implementation), but a higher or lower value can be set by the user.

For a particle of energy $E$, the mean free path for interacting via a given process is calculated as:

$$\lambda = {1\over{\Sigma_i\\ \sigma_{i}(E)\cdot n_i}}$$ (11.2)

where $\sigma_{i}(E)$ is the microscopic integrated cross-section of the process considered at energy $E$, and $n_i$ is the atomic density of the $i-th$ element contributing to the material composition. The sum runs over all the elements of which the material is composed. The cross sections are determined as described in this section. An exception to this method is the implementation of the chemical effect on hadron/ion stopping powers for a set of materials.

Sampling of Relevant Physics Quantities

The final state products of the processes are generated by sampling relevant physical quantities, such as energies and angular distributions of secondaries, from distributions derived from theoretical models and evaluated data. The energy dependence of the parameters which characterize the distributions is taken into account either by direct interpolation of the data available in the libraries, or by interpolation of values obtained from fits to the data.

When generating the final state, an atom of the material in which the interaction occurs is randomly selected and atomic de-excitation is simulated.

Secondaries which would be produced with energies below their user defined production threshold are not created and their energy is deposited locally.

Status of the document

30.09.1999 created by Alessandra Forti
07.02.2000 modified by Véronique Lefébure
08.03.2000 reviewed by Petteri Nieminen and Maria Grazia Pia
04.12.2001 reviewed by Vladimir Ivanchenko
26.01.2003 minor re-write by D.H. Wright .

Bibliography

1. ``Geant4 Low Energy Electromagnetic Models for Electrons and Photons", J.Apostolakis et al., CERN-OPEN-99-034(1999), INFN/AE-99/18(1999)
2. V.N. Ivanchenko et al., GEANT4 Simulation of Energy Losses of Slow Hadrons, CERN-99-121, INFN/AE-99/20, (September 1999).
3. S. Giani et al., GEANT4 Simulation of Energy Losses of Ions, CERN-99-300, INFN/AE-99/21, (November 1999).
4. ``EPDL97: the Evaluated Photon Data Library, '97 version", D.Cullen, J.H.Hubbell, L.Kissel, UCRL-50400, Vol.6, Rev.5
5. ``Tables and Graphs of Electron-Interaction Cross-Sections from 10 eV to 100 GeV Derived from the LLNL Evaluated Electron Data Library (EEDL), Z=1-100" S.T.Perkins, D.E.Cullen, S.M.Seltzer, UCRL-50400 Vol.31
6. ``Tables and Graphs of Atomic Subshell and Relaxation Data Derived from the LLNL Evaluated Atomic Data Library (EADL), Z=1-100" S.T.Perkins, D.E.Cullen, M.H.Chen, J.H.Hubbell, J.Rathkopf, J.Scofield, UCRL-50400 Vol.30
7. H.H. Andersen and J.F. Ziegler, The Stopping and Ranges of Ions in Matter. Vol.3, Pergamon Press, 1977.
8. J.F. Ziegler, The Stopping and Ranges of Ions in Matter. Vol.4, Pergamon Press, 1977.
9. J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Ranges of Ions in Solids. Vol.1, Pergamon Press, 1985.
10. ICRU (A. Allisy et al), Stopping Powers and Ranges for Protons and Alpha Particles, ICRU Report 49, 1993.
11. J.H. Scofield, ``Radiative Transitions", in ``Atomic Inner-Shell Processes", B.Crasemann ed. (Academic Press, New York, 1975),pp.265-292.
12. http://www.nea.fr/html/dbdata/nds_evaluated.htm
13. ``New Photon, Positron and Electron Interaction Data for Geant in Energy Range from 1 eV to 10 TeV", J. Stepanek, Draft to be submitted for publication